Recently, graph neural networks (GNNs) have become the de-facto standard used in many LoG tasks due to their super empirical performance [1]}, [2]}. Researchers often attribute such success to non-linearity in GNNs which associates them with great expressive power [3]}, [4]}. GNNs can approximate a wide range of functions defined over graphs [5]}, [6]}, [7]} and thus excel in predicting, e.g., the free energies of molecules [8]}, which are by nature non-linear solutions of some quantum-mechanical equations. However, for node classification tasks, many studies have shown that non-linearity to control the exchange of features among neighbors seems not that crucial. For example, many works use linear propagation of node attributes over graphs [9]}, [10]}, and others recommend adding non-linearity while only to the transformation of initial node attributes [11]}, [12]}, [13]}. Both cases achieve comparable or even better performance than other models with complex nonlinear propagation, such as using neighbor-attention mechanism [14]}. Recently, even in the complicated heterophilic setting where nodes with same labels are not directly connected, linear propagation still achieves competitive performance [15]}, [16]}, compared with the models with nonlinear and deep architectures [17]}, [18]}.
